Angular Acceleration vs Tangential Acceleration

In summary: So the points closer to the axis will have a higher acceleration, and the points further away will have a lower acceleration.
  • #1
Telanor
3
0
Im a little fuzzy on the difference between the two. If you look at the attached picture, if that force stays with the object as it rotates, like a hand pushing in the same spot, would that force cause an angular acceleration?
 

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  • #2
Since the force exerts a torque about the object's center of mass, it will produce an angular acceleration about the center of mass. The force will also produce an acceleration of the object's center of mass.
 
  • #3
Hey Telanor,

If the mass was fixed where represented by the point in your diagram, then the force will only produce angular accleration, as a constant force will produce acceleration around that point.

If the mass isn't fixed, the mass will exhibit both rotational and translational movement and acceleration.
 
  • #4
Ok, let's keep things simple. Way more simple. Draw a line on the box. That line will rotate an angle theta as you apply the force. That angle will get bigger and biger as you keep on applying the force. The rate at which that angle gets bigger is the angluar velocity. Same deal for the angular acceleration.

NOW, each point on the body will have a DIFFERENT tangential velocity. It will depend on how far out it is-i.e. the radius. At the very center of rotation, the tangential velocity will be zero. As you move further out, it will increase. This is because it is proportional to radius.

Consider this. All points on the body are rigid. As it sweeps an angle, let's say theta, all the points rotate. But the points on the OUTTER most edge must sweep a BIGGER circle in the same amount of time, hence they must have a higher TANGENTIAL acceleration.
 
  • #5
If that dot in the center of your diagram represents a fixed axis about which the object is free to rotate (no friction, of course), then it's a much simpler situation. (You didn't mention any fixed axis in your original post.)

In that case the force exerts a constant torque about the center, which produces a constant angular acceleration. The tangential acceleration of each point of the object depends on its distance from the axis: [itex]a_t = \alpha r[/itex].
 

What is the difference between angular acceleration and tangential acceleration?

Angular acceleration is the rate of change of angular velocity, which is the speed at which an object is rotating. Tangential acceleration, on the other hand, is the rate of change of tangential speed, which is the speed at which an object is moving along a circular path. In simpler terms, angular acceleration is related to rotation, while tangential acceleration is related to circular motion.

How are angular acceleration and tangential acceleration related?

Angular acceleration and tangential acceleration are closely related as they both involve changes in speed. In fact, tangential acceleration is often used to calculate angular acceleration, as tangential speed and angular speed are directly proportional.

What is the unit of measurement for angular acceleration and tangential acceleration?

The unit of measurement for angular acceleration is radians per second squared (rad/s²), while the unit for tangential acceleration is meters per second squared (m/s²).

How does angular acceleration affect the motion of an object?

Angular acceleration can affect the motion of an object by changing its angular velocity, which in turn affects its rotational speed and direction. An object with a higher angular acceleration will rotate faster, while an object with a lower angular acceleration will rotate slower.

Can an object have both angular acceleration and tangential acceleration at the same time?

Yes, an object can have both angular acceleration and tangential acceleration at the same time. For example, a car moving along a circular track will have both a tangential acceleration as it speeds up or slows down, and an angular acceleration as it changes its direction of motion.

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